In aerobic microorganism culture, it has been observed that conventional bioreactors lead to disadvantages associated with oxygen limitation. To solve this problem it was designed, built and tested a bioreactor prototype with external aerator. This system allowed increasing the speed of oxygen transfer from gas phase to liquid phase, overcoming the limitation of oxygen. However, this new configuration doesnt have theoretical or empirical models to predict the oxygen transfer by calculating the global volumetric coefficient of transfer of oxygen (KLa). In that way, this paper proposed the use of dimensional analysis (Buckinghams Pi Theorem), as a tool to evaluate the effect of various operating variables, fluid properties and geometrical dimensions involved in the process over KLa. After developing the proposed analysis, we found a correlation of 0.89 between the values generated by the model and the avai- lable experimental data. It was found that the main variables which affect the coefficient KLa are: the medium flow flowing through the external aerator called recirculation flow, the pressure in the external aerator, and the stirring speed.